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H.H. Khudher, A.K. Hasan, F.I. Sharrad
doi: 10.15407/ujpe62.02.0152
H.H. KHUDHER,1 A.K. HASAN,1 F.I. SHARRAD 2
1 Department of Physics, Faculty of Education for Girls, University of Kufa(31001 Najaf, Iraq; e-mail: fadhil.altaie@gmail.com)
2 Department of Physics, College of Science, University of Kerbala(56001 Karbala, Iraq; e-mail: fadhil.altaie@gmail.com)
CALCULATION OF ENERGY LEVELS,TRANSITION PROBABILITIES, AND POTENTIALENERGY SURFACES FOR 120β126XeEVEN-EVEN ISOTOPES
PACS 21.60.Ev, 27.70.+q,23.20.-g, 23.20.Lv
The interacting boson model (IBM-1) is used to calculate the energy levels, transition proba-bilities π΅(πΈ2), and potential energy surfaces of some even 120β126Xe isotopes. The theoreticalvalues are in good agreement with the experimental data. The potential energy surface is oneof the nucleus properties, and it gives a final shape of nuclei. The contour plot of the poten-tial energy surfaces shows that the 120β126Xe nuclei are deformed and have πΎ-unstable-likecharacters.K e yw o r d s: IBM-1, energy levels, π΅(πΈ2) values, potential energy surface, Xe isotopes.
1. IntroductionThe interacting boson model represents an importantstep to understand the nuclear structure. It intro-duces a simple Hamiltonian capable of describing col-lective nuclear properties through an extensive rangeof nuclei, and it is based on somewhat general al-gebraic group theoretical methods [1, 2]. The inter-acting boson model-1 (IBM-1) is a valuable interac-tive model developed by Iachello and Arima [3, 4]. Ithas been efficient in describing the collective nuclearstructure of the medium-mass nuclei, low-lying states,and electromagnetic transition rates. The interactingboson model defines the six-dimensional space and isdescribed by in terms of the unitary group π(6).
There are three dynamical symmetry limits of π(6)known as a spherical vibrator, symmetric rotor, andπΎ-unstable rotor which are labeled by π(5), ππ(3),and π(6), respectively [5, 6]. Xenon isotopes belongto a very exciting, but complex region of the Periodictable known as the transition region. The xenon iso-topes can exhibit the excitation spectra close to theπ(6) symmetry. Xenon isotopes are in a typical tran-sition region of nuclei, in which the nuclear structurevaries from that of a spherical nucleus to a deformednucleus [7]. For the xenon series of isotopes, the orig-inal version of IBM-1 had been used in calculating
cβ H.H. KHUDHER, A.K. HASAN, F.I. SHARRAD, 2017
the energy levels of the positive parity low-lying nu-clei [8]. For the even 120β126Xe isotopes with neutronnumber (66 6 π 6 72), the energy ratio (πΈ4+/πΈ2+)is nearly 2.5 and indicates πΎ-soft shapes. In the re-cent years, many works had been done on the struc-ture of xenon isotopes; S.A. Eid and S.M. Diab [9]calculated the potential energy surfaces, (π π½, πΎ) fora series of xenon isotopes 122β134Xe, energy levels,and reduced transition probabilities π΅(πΈ2), by usingIBM-1. These results were compared with the exper-imental data and found sensible agreement. K. Po-morski and B. Nerlo-Pomorska [10] studied the quickrotation for the even-even Zn, Mo, Sn, Te, Xe, Ba,Ce, and Nd isotopes and presented the typical prop-erties for high-spin states as well. B.S. Rawat andP.K. Chattopadhyay [11] analyzed the spectra ofthe xenon isotopes by the π(6) symmetry break-ing and used the excitation energies of the states0+2 and 0+3 under a noticeable breaking of the sym-metry. H. Kusakari and M. Sugawara [12] calculatedthe energy levels, backbendings in the yrast bands,and reduced transition probabilities for the positive-parity states of 122β130Xe within the framework ofthe interacting boson model. B. Saha et al. [13] mea-sured the π΅(πΈ2) and π΅(π1) values for the isotopeof 124Xe. H. Kusakari et al. [14] studied the high-spin states in the even 122β130Xe by in-beam πΎ-rayspectroscopy. The 10+2 level in 126Xe was assigned
152 ISSN 2071-0194. Ukr. J. Phys. 2017. Vol. 62, No. 2
Calculation of Energy Levels, Transition Probabilities, and Potential Energy Surfaces
near the 10+1 level, and the 14+2 level was too. In theyrast bands, the backbending phenomena were de-tected systematically in the even 122β130Xe isotopes.L. Coquard et al. [15] investigated low-lying collectivestates in 126Xe via the 12C(126Xe, 126Xe*) projectileCoulomb excitation reaction at 399 MeV. M. Serris etal. [16] used the EUROGAM array to investigate thehigh-spin states in 122Xe by πΎ β πΎ coincidence mea-surements. The reaction 96Zr (30Si, 4π) 122Xe wasused to populate states of 122Xe at a beam energy of135 MeV. The new structures of competing π΅(π1)to π΅(πΈ2) transitions were observed. In the π(6)-likenuclei, the triaxial deformation of the even-even Xe,Ba, Ce isotopes had been studied.
The aim of the present work is to study the energylevels, transition probabilities π΅(πΈ2), and the poten-tial energy surfaces of some even 120β126Xe isotopeswithin the framework of IBM-1 and to compare theresults with the experimental data. Furthermore, wewill describe the nuclear structure for Xe isotopes, byusing the potential energy surface πΈ(π, π½, πΎ).
2. Interacting Boson Model (IBM-1)
The Interacting Boson Model has become one of themost intensively used nuclear models, due to its abil-ity to describe the changing low-lying collective prop-erties of nuclei across the entire major shell with asimple Hamiltonian. In IBM-1, the low-lying collec-tive properties of even-even nuclei were described interms of a system of interacting π -bosons (πΏ = 0) andπ-bosons (πΏ = 2) [18]. The underlying structure ofthe six-dimensional unitary group U(6) of the modelleads to a simple Hamiltonian capable of describingthe three dynamical symmetries π(5), ππ(3), andπ(6) [4, 18]. The most general IBM Hamiltonian canbe expressed as [19, 20]:
π» = ππ (π β Β· π ) + ππ(π
β Β· π) +β
πΏ=0,2,4
1
2(2πΏ+ 1)1/2πΆπΏ Γ
Γ[[πβ Γ πβ ](πΏ) Γ [πΓ π](πΏ)
](0)+
1β2π2
[[πβ Γ πβ ](2)Γ
Γ [πΓ π ](2) + [πβ Γ π β ](2) Γ [πΓ π](2)](0)
+
+1
2π0
[[πβ Γ πβ ](0) Γ [π Γ π ](0) + [π β Γ π β ](0) Γ
Γ [πΓ π](0)](0)
+1
2π’0
[[π β Γ π β ](0) Γ [π Γ π ](0)
](0)+
+π’2
[[πβ Γ π β ](2) Γ [πΓ π ](2)
](0), (1)
where (π β , πβ ) and (π , π) are the creation and an-nihilation operators for π - and π-bosons, respec-tively [18]. This Hamiltonian contains two one-bodyterms specified by the parameters (ππ and ππ) andseven two-body terms specified by the parameters[πΆπΏ (πΏ = 0, 2, 4), π£πΏ (πΏ = 0, 2), π’πΏ (πΏ = 0,2)], where ππ and ππ are the single-boson energies,and ππΏ, π£πΏ and π’πΏ describe the two-boson inter-actions. However, it turns out that, for a fixed bo-son number π , only one of the one-body terms andfive of the two-body terms are independent, as itcan be seen by noting π = ππ + ππ. There areseveral corresponding ways to write the Hamilton-ain, one of these forms is the multipole expansion[18, 19, 20]
οΏ½οΏ½=ποΏ½οΏ½π+π0πΒ·π+π1οΏ½οΏ½Β·οΏ½οΏ½+π2οΏ½οΏ½Β·οΏ½οΏ½+π3π3 Β·π3+π4π4 Β·π4.
(2)
The operators are defined by the following equations:
οΏ½οΏ½π = (πβ π), (3)
π = 1/2[π, πβ π , π ], (4)
οΏ½οΏ½ =β10[πβ Γ π]1, (5)
οΏ½οΏ½ = [πβ Γ π + π β Γ π](2) + π[πβ Γ π](2), (6)
ππ = [πβ Γ π](π), (7)
π = ππ + ππ , (8)
where οΏ½οΏ½π, π, οΏ½οΏ½, οΏ½οΏ½, and ππ are the total numberof π-bosons, pairing, angular momentum operator,quadrupole, octupole (π = 3), and hexadecapole(π = 4) operators, respectively, π is the boson energy,and π (CHI) is the quadrupole structure parameter,which takes the values 0 and Β±
β72 [18, 19, 20]. The
parameters π0, π1, π2, π3, and π4 designate the pair-ing strength, angular momentum, quadrupole, oc-tupole, and hexadecapole interactions between thebosons. The π(6) symmetry of IBM-1 is based onthe chain π(6) β π(6) β π(5) β π(3) of the nestedsubalgebra with quantum numbers π , π, and πΏ, re-spectively [18]. The energies of collective states in theO(6) limit are given by [18];
πΈ(π, π, πΏ) +π΄(π β π)(π + π + 4)+
+π΅π(π + 3) + πΆπΏ(πΏ+ 1), (9)
where (π΄ = π0/4, π΅ = π3/2, πΆ = π1 β π3/10), π isthe number of bosons π=π , π β 2, π β 4, ..., 0 and
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H.H. Khudher, A.K. Hasan, F.I. Sharrad
Fig. 1. (Color Online) Comparison the IBM-1 calculations with the available experimental data [22-24] for120β122Xe nuclei
Table 1. Adopted values of the parameters used in the IBM-1 calculations. All parametersare given in MeV, except π and CHI (CHI is a constant dependent on the dynamical symmetry)
Isotope π π π0 π1 π2 π3 π4 CHI
120Xe 10 0.0000 0.082609 0.012133 0.0000 0.178435 0.0000 0.0000122Xe 9 0.0000 0.114918 0.015834 0.0000 0.168768 0.0000 0.0000124Xe 8 0.0000 0.14099 0.019322 0.0000 0.170068 0.0000 0.0000126Xe 7 0.0000 0.164235 0.022538 0.0000 0.181002 0.0000 0.0000
π = 0, 1, ..., π. πΏ takes on the πΏ = 2π, 2π β 2, ...,π + 1, π, where π is a positive integer; π = π β 3πΞfor πΞ = 0, 1, 2, ... [20].
3. Results and Discussion
The calculated results can be discussed separately forthe energy levels, reduced probability of πΈ2 transi-tions, and potential energy surfaces.
3.1. Energy Levels
The energy levels of some even 120β126Xe isotopeshave been calculated, by using the experimentalenergy ratios πΈ2 :πΈ4 :πΈ6 :πΈ8 = 1 : 2.5 : 4.5 : 7 [21]within the framework of IBM-1. It has been foundthat the 120β126Xe isotopes are deformed nuclei, andthey have a dynamical symmetry π(6). For the anal-ysis of excitation energies of xenon isotopes, it is triedto keep a minimum number of free parameters in theHamiltonian. The adopted Hamiltonian is expressing
as [20]
οΏ½οΏ½ = π0π Β· π + π1οΏ½οΏ½ Β· οΏ½οΏ½+ π3π3 Β· π3. (10)
In IBM-1, the even 120β126Xe isotopes (π = 54)have a number of proton boson particles equal to 2,and a number of neutron boson holes varies from 5to 8, respectively. The Table 1 shows that the pa-rameters used in the present work. The calculatedground π-band, π½-band, and πΎ-band and the experi-mental data on low-lying states are plotted in Figs. 1and 2 for even-even 120β126Xe isotopes. These figuresshow that the IBM calculations of the energies, spin,and parity are in good agreement with the experi-mental values [22β26]. However, it is deviated in thehigh-spin energies of the experimental data. Levelswith β( )β correspond to the cases, for which the spinand/or parity of the corresponding states are not wellestablished experimentally.
Furthermore, from Fig. 1, the levels 5+1 , 8+2 , 10+2 ,2+3 , 4+3 , and 6+3 with energies of 2.326, 2.996, 3.850,
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Fig. 2. (Color Online) Comparison the IBM-1 calculations with the available experimental data [22, 25, 26] for124β126Xe nuclei
Table 2. π½2-bands for Xe isotopes (in MeV). The experimental data are taken from [22β26]
π½π
120Xe 122Xe 124Xe 126Xe
IBM-1 exp. IBM-1 exp. IBM-1 exp. IBM-1 exp.
0+ 1.6051 1.62325 1.5210 2.26444 * 1.5300 1.68991 1.6290 1.760542+ 1.9746 1.92411 * 2.3597 2.3431 2.3938 2.51947 2.5607 2.455334+ 2.4000 2.44842 * 2.6500 β 2.8450 β 3.0316 2.9739 *
6+ 3.1667 β 3.4719 β 3.7456 β 4.0345 β8+ 4.0663 β 4.4544 β 4.8016 β 5.2540 β
10+ 5.0987 β 5.5975 β 6.2030 β β β
1.231, 1.688, and 2.275 MeV, respectively, for 120Xeisotope, and 12+1 , 14+1 , 2+2 , 3+1 , 4+2 , 5+1 , 6+2 , 7+1 , 8+2 ,9+1 , and 10+2 with energies of 4.3992, 5.6945, 0.8387,1.5084, 1.500, 2.3345 , 2.3219, 3.3212, 3.3044, 4.4685,and 4.4145 MeV, respectively, for 122 Xe isotope cor-respond to the cases, for which the spin and/or par-ity of the corresponding states are not well estab-lished experimentally [22-24]. From Fig. 2, the lev-els 12+1 , 14+1 , 9+1 , 10+2 , 4+3 , 6+3 , and 8+3 with ener-gies of 4.9488, 6.4330, 4.7970, 4.8430, 2.1650, 2.8956,and 3.8146 MeV for 124Xe isotope, and 8+2 , 9+1 , and6+3 with energies of 3.9404, 5.2875, and 3.1295 MeVfor 126Xe isotope correspond to the cases, for whichthe spin and/or parity of the corresponding states arenot well established experimentally [22, 25, 26]. Theπ½2-bands calculated in this work are shown in Ta-ble 2. This table presents the comparison between of
the IBM-1 calculations and the experimental energylevels of 120β126Xe isotopes. From this comparison, agood agreement between the experimental data andthe IBM-1 calculation is seen. Levels with β*β corre-spond to cases, for which the spin and/or parity ofthe corresponding states are not well established ex-perimentally.
3.2. The B(E2) Values
New information can be founded, by studying thereduced transition probabilities B(πΈ2). The reducedmatrix elements of the πΈ2 operator have the form [18,27, 28]
π (πΈ2) = πΌ2[πβ π + π β π](2) + π½2[π
β π](2) =
= πΌ2([πβ π + π β π](2) + π[πβ π](2)) = ππ΅οΏ½οΏ½, (11)
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H.H. Khudher, A.K. Hasan, F.I. Sharrad
Fig. 3. Color Online) Potential energy surface in the πΎ β π½ plane for 120β126Xenuclei
where πΌ2 and π½2 are two parameters, π½2 = ππΌ2, πΌ2 == ππ΅ , where ππ΅ is the effective charge, and
οΏ½οΏ½ = ([πβ π + π β π] + π[πβ π](2), (12)
where οΏ½οΏ½ is the quadrupole operator. The electrictransition probabilities π΅(πΈ2) are defined in termsof reduced matrix elements as [18, 30]
π΅((π2), π½π β π½π ) =1
2π½π
β¨π½π β π (πΈ2) β π½πβ©
2. (13)
The values ππ΅ are estimated to reproduce the experi-mental π΅(πΈ2; 2+1 β 0+1 ) and are given in Table 3. Inaddition, the comparisons of the calculated π΅(πΈ2)values with the experimental data [22β26] are givenin Table 4 for all nuclei under study.
Table 4 shows that, in general, most of the calcu-lated results in IBM-1 are reasonably consistent withthe available experimental data, except for few casesthat deviate from the experimental data.
Table 3. Effective charge usedto reproduce π΅(πΈ2) values for 120β126Xe Nuclei
π΄ π πB (eb)
120Xe 10 0.1112122Xe 9 0.1094124Xe 8 0.10126Xe 7 0.10
3.3. Potential energy surface πΈ(π,π½, πΎ)
The potential energy surface gives a final shape to thenucleus that corresponds to the Hamiltonian [31] inthe equation [20]
πΈ(π,π½, πΎ) = β¨π, π½, πΎ|π»|π, π½, πΎβ©/β¨π, π½, πΎ|π, π½, πΎβ©.(14)
The expectation value of the IBM-1 Hamiltonian withthe coherent state (|π, π½, πΎβ©) is used to construct theIBM energy surface [19, 20]. The state is a productof boson creation operators,
(πβ π), with |π, π½, πΎβ© = 1/βπ !(πβ π)
π |0β©, (15)
πβ π = (1 + π½2)β1/2{π β + π½[cos πΎ(πβ 0)+
+β1/2 sin πΎ(πβ 2 + πβ β2]
}. (16)
The energy surface, as a function of π½ and πΎ, has beengiven by [18]
πΈ(π, π½, πΎ) =ππππ½
2
(1 + π½2)+
(π(π + 1)
(1 + π½2)2Γ
Γ (πΌ1π½4 + πΌ2π½
3 cos 3πΎ + πΌ3π½2 + πΌ4), (17)
where the πΌπ are related to the coefficients πΆπΏ, π2,π0, π’2, and π’0 of Eq (1), and π½ is a measure of thetotal deformation of a nucleus. For π½ = 0, the shape
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Calculation of Energy Levels, Transition Probabilities, and Potential Energy Surfaces
Table 4. π΅(πΈ2) values for 120β126Xe nuclei (in e2b2)
π½π β π½π
120Xe [22, 23] 122Xe [22, 24]π½π β π½π
124Xe 126Xe
IBM-1 exp. IBM-1 exp. IBM-1 exp. [22, 25, 32] IBM-1 exp. [22, 26, 32]
2+1 β 0+1 0.3460 0.346(22) 0.2800 0.280(12) 2+1 β 0+1 0.1920 0.192(12) 0.1540 0.154(5)2+2 β 0+1 0.0483 β 0.0392 β 2+2 β 0+1 0.0270 0.0026(5) 0.0217 0.002(7)2+2 β 2+1 0.4766 β 0.3829 β 4+1 β 2+1 0.2600 0.2484(7) 0.2057 0.267(3)4+1 β 2+1 0.4766 0.412(28) 0.3829 0.409(22) 4+2 β 2+1 0.0206 0.00025 0.0160 0.0015(3)4+2 β 2+1 0.0385 β 0.0307 β 4+2 β 2+2 0.1467 0.254(92) 0.1135 0.1355(16)6+1 β 4+1 0.5272 0.415(63) 0.4188 0.396(144) 6+1 β 4+1 0.2800 0.323(29) 0.2167 0.315(41)6+2 β 4+1 0.0295 β 0.228 β 6+2 β 4+1 0.0147 β 0.0108 β6+1 β 4+2 0.0245 β 0.0211 β 4+2 β 6+1 0.0228 β 0.0204 β8+1 β 6+1 0.5347 0.341(59) 0.4177 0.288(179) 8+1 β 6+1 0.2727 0.243(77) 0.2036 β8+1 β 6+2 0.0289 β 0.0225 β 8+1 β 6+2 0.0195 0.0179 β
10+1 β 8+1 0.5133 0.324(53) 0.3912 0.432(179) 10+1 β 8+1 0.2462 0.0772(1) 0.1731 β10+2 β 10+1 0.0046 β 0.0032 β 12+1 β 10+1 0.2040 0.202(44) 0.1280 β12+1 β 10+1 0.4695 0.292(46) 0.3446 β 2+2 β 2+1 0.2600 0.118(22) 0.2057 0.162(1)12+2 β 10+2 0.3042 0.246(246) 0.1532 β 2+3 β 2+1 0.0031 0.0022(2) 0.0026 0.000414+1 β 12+1 0.4070 0.282(42) 0.2809 β 4+2 β 4+1 0.1333 0.125(47) 0.1032 0.1062(14)16+1 β 14+1 0.3278 0.42(14) 0.2015 β 6+2 β 6+1 0.0868 β 0.064818+1 β 16+1 0.2330 0.598(105) 0.1077 β 10+2 β 10+1 0.0394 β 0.02476+2 β 6+1 0.1701 β 0.1329 β 3+1 β 4+1 0.0799 0.096(44) 0.0618 0.08293+1 β 4+1 0.1507 β 0.1197 β 3+1 β 2+1 0.0281 0.0029(6) 0.0218 0.0034(2)3+1 β 2+1 0.0525 β 0.0419 β 3+1 β 2+2 0.2000 0.3454 0.1548 0.2091(24)3+1 β 2+2 0.3766 β 0.2992 β
is spherical, and it is distorted, when π½ = 0. The pa-rameter πΎ is the amount of deviation from the focussymmetry and correlates with the nucleus shape. IfπΎ = 0, the shape is prolate, and if πΎ = 60 the shapebecomes oblate. In Fig. 3, the contour plots in theπΎ β π½ plane resulting from πΈ(π, π½, πΎ) are shown for120β126Xe isotopes. For most of the considered Xe nu-clei, the mapped IBM energy surfaces are of the tri-axial shape. This shape is associated with interme-diate values 0 < πΎ < 60. The triaxial deformationhelps to understand the prolate-to-oblate shape tran-sition that occurs in the considered Xe isotopes. TheXe nuclei considered here do not display any rapidstructural change, but remain πΎ-soft. This evolutionreflects the triaxial deformation, as one approachesthe neutron shell closure π = 82.
4. Conclusions
The energy levels (positive parity), reduced proba-bilities of πΈ2 transitions, and potential energy sur-faces for 120β126Xe nuclei have been calculated within
the framework of the interacting boson model-1. Thepredicted low-lying levels (energies, spins, and par-ities) and the reduced probabilities of E2 transi-tions are reasonably consistent with the experimen-tal data. For the even 120β126X isotopes, the potentialenergy surfaces show that all nuclei are deformed andare characterized by the dynamical symmetry π(6).
We thank University of Kufa, Faculty of Educationfor Girls, Department of Physics and University ofKerbala, College of Science, Department of Physicsfor supporting this work.
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Π₯.Π₯.Π₯ΡΠ΄Π΅Ρ, Π.Π.Π₯Π°ΡΠ°Π½, Π€.I.Π¨Π°ΡΡΠ°Π΄
Π ΠΠΠ ΠΠ₯Π£ΠΠΠ Π IΠΠIΠ ΠΠΠΠ ΠIΠ, IΠΠΠIΠ ΠΠΠ‘Π’ΠΠΠΠΠ ΠΠ₯ΠΠΠ£, ΠΠΠΠΠ Π₯ΠΠΠ¬ ΠΠΠ’ΠΠΠ¦IΠΠΠ¬ΠΠΠ ΠΠΠΠ ΠIΠΠΠΠ― ΠΠΠ ΠΠ-ΠΠΠ ΠΠΠ₯ 120β126Xe IΠΠΠ’ΠΠIΠ
Π Π΅ Π· Ρ ΠΌ Π΅
Π£ ΠΌΠΎΠ΄Π΅Π»i Π²Π·Π°ΡΠΌΠΎΠ΄iΡΡΠΈΡ Π±ΠΎΠ·ΠΎΠ½iΠ² ΡΠΎΠ·ΡΠ°Ρ ΠΎΠ²Π°Π½ΠΎ ΡiΠ²Π½i Π΅Π½Π΅ΡΠ³iΡ,ΠΉΠΌΠΎΠ²iΡΠ½ΠΎΡΡi ΠΏΠ΅ΡΠ΅Ρ ΠΎΠ΄iΠ² π΅(πΈ2) i ΠΏΠΎΠ²Π΅ΡΡ Π½i ΠΏΠΎΡΠ΅Π½ΡiΠ°Π»ΡΠ½ΠΎΡ Π΅Π½Π΅Ρ-Π³iΡ Π΄Π΅ΡΠΊΠΈΡ ΠΏΠ°ΡΠ½ΠΈΡ 120β126Xe iΠ·ΠΎΡΠΎΠΏiΠ² Ρ Ρ ΠΎΡΠΎΡiΠΉ Π²iΠ΄ΠΏΠΎΠ²iΠ΄Π½ΠΎ-ΡΡi Π΄ΠΎ Π΅ΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ°Π»ΡΠ½ΠΈΡ Π΄Π°Π½ΠΈΡ . ΠΠΎΠ²Π΅ΡΡ Π½Ρ ΠΏΠΎΡΠ΅Π½ΡiΠ°Π»ΡΠ½ΠΎΡΠ΅Π½Π΅ΡΠ³iΡ ΡΠΊ ΠΎΠ΄Π½Π° Π· Ρ Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΡΡΠΈΠΊ ΡΠ΄ΡΠ° Π²ΠΈΠ·Π½Π°ΡΠ°Ρ ΠΊiΠ½ΡΠ΅Π²Ρ ΡΠΎΡ-ΠΌΡ ΡΠ΄Π΅Ρ. ΠΠΎΠ½ΡΡΡΠ½ΠΈΠΉ Π³ΡΠ°ΡiΠΊ ΠΏΠΎΠ²Π΅ΡΡ ΠΎΠ½Ρ ΠΏΠΎΡΠ΅Π½ΡiΠ°Π»ΡΠ½ΠΎΡ Π΅Π½Π΅ΡΠ³iΡΠΏΠΎΠΊΠ°Π·ΡΡ, ΡΠΎ 120β126Xe ΡΠ΄ΡΠ° Π΄Π΅ΡΠΎΡΠΌΠΎΠ²Π°Π½i i Π½Π΅ΡΡΠ°Π±iΠ»ΡΠ½i Π΄ΠΎ πΎ-ΡΠΎΠ·ΠΏΠ°Π΄iΠ².
158 ISSN 2071-0194. Ukr. J. Phys. 2017. Vol. 62, No. 2
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